Choose ten problems from p. 424/1-88 and/or p. 472/16-66 and/or p. 532/10-22
Prepare for Unit 4 test next class by going through IW #1–#13.
Wednesday, May 16th, 2012
Today was project day.
IW:
Work on your project for an hour.
Monday, May 14th, 2012
We took the IW #13 quiz and those that wanted then took the re-quiz. Others worked on the project.
IW:
Work on your project for an hour.
Thursday, May 10th, 2012
We warmed up with some IW #13 questions- without technology. We then discussed the IW and corrected the quiz. We spent the remainder of class working on the project.
IW:
Work on your project for an hour. Monday's IW #13 quiz will be open IW, closed technology. Make sure you've finished that investigation.
If you didn't do well on Tuesday's quiz, you may re-quiz on Monday.
Tuesday, May 8th, 2012
After the IW quiz, we worked on IW #13 in groups. The assessment on IW #13 will be a quiz *without* technology where you will need to sketch graphs, write equations, find intercepts, etc. of polar graphs from IW #13. You will be able to use IW #13 on the quiz, so be sure you have thoroughly investigated the polar graphs and taken good notes. Feel free to also bring any questions to next class.
IW:
Choose your Q4 project and start your Google Doc. Name it "Q4 Your Name" and share it with obrienbluester@gmail.com. Work on it for one hour.
Friday, May 4th, 2012
We worked on IW #13, a polar graphing investigation.
We began class with a vector warm-up and then took a further look at addition and subtraction geometrically with this applet. We discussed the IW and then examined polar coordinates and polar graphing.
IW #12:
p. 492/7, 9, 11, [19, 21, 23, 25 by making tables and plotting points], [39 using the graphing calculator]
IW quiz postponed but IW still due next class.
Monday, April 30th, 2012
We by correcting the IW quiz and discussing the cool complex number assignment. This led us to a discussion of vectors.
IW #11:
p. 469/1, 7, 9, 11, 13, 25, 29, 33
Thursday, April 26th, 2012
We began class with the IW quiz. We then went over the IW questions, focusing on geometric interpretations of De-Moivre's Theorem.
We began class by going over the IW quiz. We then discussed the IW, focusing on how to use the calculator as well as how diagrams and reasoning are better than formulas. We then worked on the IW #9 packet.
We began class with the IW quiz. We then went over the IW questions and learned how trigonometry is used with complex numbers.
IW #8:
p. 450/7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31
Wednesday, April 11th, 2012
We began by finding an enveloping function for the sum of two sine functions which lead us to the Sum to Product identities. After we went through the proofs from IW #6, we proved a Product to Sum identity and used it to prove the identity needed in the warm-up. We also learned how to find the exact values of the first question from the Unit 4 Quiz #1 without using technology. We finished by looking at how to solve trig equations algebraically.
IW #7:
p. 423/9, 13, 15, 17, 19, 21, 23
Be ready for the IW quiz next class covering IW #1 through #6.
Monday, April 9th, 2012
We began class by proving four trig identities, proving we could do so without crying. We then went over the IW questions and the IW quiz. We spent the remainder of class working on IW #6, deriving sum/difference, double, and half angle identities.
We had our IW quiz and then worked some more on proving identities.
IW #5:
p. 407/4, 10, 14, 17, 19, 20, 21, 23, 37
IW #1 to #4 are due next class
Tuesday, April 3rd, 2012
We began class by learning about how to verify trig identities. Here are a set of guidelines to avoid tears... We spent the remainder of the class discussing the previous independent work questions.
IW #4:
p. 407/1-15 odd, 25, 27, 31, 33
Be sure IW #1 to #3 (including the IW#1 follow-up) are finished and checked before the quiz next class.
Friday, March 30th, 2012
We began with the first several questions of IW #3 and then discussed IW #2. For the remainder of class, we worked on the IW #3 sheet.
We began class by checking answers to IW #1 and discussing wave packets. We then transitioned to inverse trig relations. We used Geogebra to discover how to restrict domains to create functions. We then tried p. 395/42 and 49 from the IW, noting that inverse trig functions were just angles.
Use Geogebra to graph p. 394/11 and 12 and write a brief explanation of *why* each graph looks like it does...
Monday, March 26th, 2012
We began by finding a plausible expression to generate this graph:
We then went over the Supercorrection follow up test. We spent the remainder of the period investigating trig wave functions with the IW packet.
We took the follow up test and finished the project.
IW:
Finish your project.
Tuesday, March 20th, 2012
We worked on the project.
IW:
Study for the follow-up test. Blank copy here: U3Tpap.pdf
Finish your project- you will have the rest of next class to work as well.
Thursday, March 15th, 2012
We worked on the projects.
IW:
Work on your project for an hour.
Be sure you've got work done on your Google Doc by Sunday when Mr. O'Brien takes a look at your project.
Tuesday, March 13th, 2012
We worked on Supercorrections.
IW:
Finish your Supercorrections.
Friday, March 9th, 2012
We worked on Supercorrections.
IW:
Work one hour on your Supercorrections.
Wednesday, March 7th, 2012
We finished the test and began Supercorrections.
IW:
Work one hour on your Supercorrections.
Monday, March 5th, 2012
Today was test day!
IW:
Read through the projects and choose one. Make a Google Doc titled Q3 Your First Name Project Name and share it with obrienbluester@gmail.com.
Thursday, March 1st, 2012
Snow day! Test postponed until Monday.
Optional IW:
Read through the projects and choose one. Make a Google Doc titled Q3 Your First Name Project Name and share it with obrienbluester@gmail.com.
Tuesday, February 28th, 2012
Today was our revision day. We warmed up by finding a couple plausible periodic functions from graphs. We then corrected the quiz and went over IW questions and general revision. We finished by watching the Tau Day video again and discussing the trig segments.
IW #11:
p. 369/Choose any ten questions.
Friday, February 17th, 2012
We began class with the quiz: Quizlet question #1. We then proved the Law of Cosines and went over the IW. We also took a look at the Tau Manifesto.
IW #10:
These ten word problems with the Law of Sines and Law of Cosines (work in your notebook so that you can submit it when the IW is due)
*Why* is the length of each trig segment the value of the corresponding function?
Why are the tangent and secant functions given the names they are?
Why are the co-function given the prefix co?
Wednesday, February 15th, 2012
We began class with this exploration in Geogebra. After proving the Law of Sines, we derived a formula for the area of a triangle given two sides and an included angle, and we discussed the IW and The Ambiguous Case (Eben's applet & Kyle's Applet). We then corrected the quiz and took a look at six trig segments in the unit circle- neato! We finished class by deriving the Law of Cosines.
IW #9:
p. 443/3, 5, 11, 13, 19, 23, 25, 27
Not optional: Watch this video. For extra credit, geek out by reading the Tau Manifesto and email Mr. O'Brien your thoughts in a paragraph.
Optional: Would you like a nice simple explanation of a problem using the Law of Sines and the Ambiguous Case? Check out this nice video.
Quiz next class through IW #8. It will be a mix of memorized values and calculator.
Monday, February 13th, 2012
We began class with the IW quiz. Following the quiz, we corrected the IW and learned a way to solve a non-right angled triangle using the Law of Sines.
IW #8:
Read about "The Ambiguous Case" of the Law of Sines online. Extra credit: find a cool applet that demonstrates this case and email it to Mr. O'B...
p. 435/3, 11, 13, 19, 21
Continue to practice with your common trig values: take another Quizlet quiz, aiming to work without your unit circle or calculator...
Thursday, February 9th, 2012
In preparation for the next quiz on which a portion will be no calculator/no unit circle, we once again began class with the little practice quiz on the six trig functions of the common angles and did a little stand-up practice. We then discussed the quiz from last class and went over IW questions. The remainder of the class was spent working trig application problems.
IW #7:
p. 367/7, 11, 15, 17, 19, 27, 29, 31, 37, 39
Quiz next class
Continue to practice with your common trig values: take another Quizlet quiz, aiming to work without your unit circle or calculator...
Tuesday, February 7th, 2012
We again began class with the little practice quiz on the six trig functions of the common angles. We then took the quiz on IW #1 and #4 and went over questions from IW #5. We then took a little break from all this heavy full circle trig by revisiting some nice, friendly right triangle trig.
IW #6:
p. 361/1-7, 21, 39, 43, 53
Continue to practice with your common trig values: take another Quizlet quiz, aiming to work without your unit circle or calculator...
Friday, February 3rd, 2012
We began class with a game of Around The World to practice our common trig values and then continued with five minutes of the little practice quiz on the six trig functions of the common angles. We then corrected the quiz and discussed the IW. We noted how trig equations can be solved with either the unit circle or a graph and how the symmetry of the trig waves along with five key points and a labeled scale makes any trig graphing task a snap. We then explored how the other four trig function graphs can be derived from the sine and cosine waves. Our discussion included a look at domain, range, period, and vertical asymptotes.
IW #5:
Watch this 7:46 minute video from PatrickJMT on how to quickly graph all six trig functions
p. 352/3, 6, 7, 9, 17, 31, 37, 51
Quiz next class- you may use your pink unit circle on this quiz (but not after that!)
Continue to practice with your common trig values: take another Quizlet quiz, aiming to work without your unit circle or calculator...
Wednesday, February 1st, 2012
We began class with a little practice quiz on the six trig functions of the common angles. This led us to a review of the trig properties from last class. We then took the quiz on IW #1 and #2 and went over questions from IW #3. We used this Geogebra sketch to explore the graphs of the sine and cosine function. We discussed period, amplitude, and even/odd, and finished by looking at transformations of the graphs.
Continue to practice with your common trig values: take another Quizlet quiz, aiming to work without your unit circle or calculator...
Monday, January 30th, 2012
We began class with a little practice quiz converting between the common degree and radian values. We then discussed the independent work, learning how easy it is to find arc length (and sector area) when working in radians. We took a closer look at the Unit Circle and how its coordinates are found and then defined the cosine and sine functions using points on this wonderful circle. We defined the other four trig functions which led to three sets of identities: the reciprocal, quotient, and Pythagorean. We finished by discussing the importance of the common trig values.
IW #3:
p. 335/5, 9, 17, 19, 27, 31, 41, 47, 49, 50
Use the ThatQuiz link on the website to do the 10 questions there
Watch this 7:18 minute video from PatrickJMT on a way to remember the unit circle values
Memorize the common radian-degree conversions: this Quizlet set may help you quiz yourself, and this circle may help you visualize the angles (you can turn off the coordinates if they get in the way)
Tuesday, January 24th, 2012
We began class with an individual reflection on the first semester, and then in groups of three or four, we came up with some pieces of advice for success in an O'Brien math classroom. We then discussed some of the midterm and introduced our new unit on trigonometry.
As tomorrow is our revision day, post *any* questions on old IW's or polynomial, rational, radical, exponential, or logarithmic functions. We will use these for the basis of our revision.
Thursday, December 8th, 2011
We warmed up and discovered some interesting ways to perceive exponential and logarithmic functions. After discussing the IW's, we corrected the quiz.
In preparation for your quiz next class, be sure you can do *all* problems from IW #1-#10 (without technology where appropriate)
Tuesday, December 6th, 2011
We began class with the quiz and then corrected the IW. This led us to a discussion of the inverse of an exponential function: a new parent function!
IW #10:
p. 292/1-7 odd, 13-33 odd, 51, 55
IW #5 to #9 due next class: be sure they are finished and corrected.
Friday, December 2nd, 2011
We began by exploring the end behavior of an interesting function: (1 + 1/x)^x. Who wins as x goes to infinity- the 1/x going to zero or the massively powerful power of x?!? We also listened to this radio segment from NPR this week. We then corrected the quiz and discussed the IW. We ended class by discussing compound interest, connecting it all back to our warm-up function.
IW #9:
p. 269/41
p. 277/32-37, 39, 41, 43, 45
Wednesday, November 30th, 2011
We began class with the quiz. After the quiz, we took a brief look at IW questions. We then thought about this question:
If a piece of paper could be folded in half fifty times, how high would the stack of paper be? For more on this problem, click here. Have you heard that it is impossible to fold a piece of paper more than eight times? If so, click here .
This led us to define our next parent function, the exponential.
IW #8:
p. 262 "Exploring with a graphing utility" (use Geogebra)
p. 268/15, 17 19, 21, 50-52
Monday, November 28th, 2011
We began class by creating a couple of rational functions. We then corrected the quiz and discussed IW #5 & #6.
IW #7:
Use Geogebra to graph x^(1/n) where n is even and where n is odd. What conclusions can you draw?
p. 255/15, 23, 25, 33, 44-47
In preparation for your quiz next class, be sure you can do *all* problems from IW #1-#6 (without technology where appropriate)
Monday, November 21st, 2011
We began class with the quiz. We discussed the IW and created some cool rational functions.
IW #6:
p. 244/3, 9, 19, 28-31, 38-40
Thursday, November 17th, 2011
We warmed up with a rational function transformation question. After correcting the quiz and discussing the IW, we explored rational functions by using Geogebra, our hand graphing skills, and our rational function building skills.
IW #5:
p. 234/9, 11, 13, 37, 39, 43, 59
In preparation for your quiz next class, be sure you can do *all* problems from IW #1-#4 (without technology where appropriate)
Tuesday, November 15th, 2011
We began class with the quiz. We looked at IW questions and the "build a polynomial" extra credit from last class, and then ended class with some notes on rational functions, including horizontal and vertical asymptotes from a graphic and numeric perspective.
IW #4:
p. 222/7, 19, 27, 39, 43, 46, 47
Thursday, November 10th, 2011
We began class with a warm up equation, finding *all* the zeros, including complex zeros. This led to some notes on complex conjugates, the Fundamental Theorem of Algebra, and multiplicity of zeros. After correcting the IW, we participated in some polynomial forming extra credit (submit your polynomials here).
IW #3:
p. 193/11, 17, 27, 29, 37, 41
p. 198/19
p. 207/25
p. 209/21, 35
Be sure to finish IW #1 and #2 in preparation for the quiz next class.
Tuesday, November 8th, 2011
We began class by using a warm-up question (photo of the board here) and IW #1 to discuss good graphing calculator viewing window tricks: using the table, using Zbox, Zfit, etc. We corrected the Supercorrection Follow-up test, took a look at Mr. O'Brien's online grade calculator, and discussed IOU's. We then discussed zeros which led to a look at the Rational Zero Test, polynomial long division and synthetic division, the Remainder Theorem, the Factor Theorem, and the complex numbers (photos of the board here, here, here, here, and here).
IW #2:
p. 171/3, 5, 17, 33
p. 183/3, 27
p. 193/7, 15, 25
If you are absent from class, be sure to read sections 3.3 to 3.5 in your textbook (no need for Horner's Algorithm). If you have questions after reading that over, be sure to stop by!
Friday, November 4th, 2011
Today was the start of our next unit. We began by creating a general 5th degree polynomial function in Geogebra and explored it. We learned some new vocabulary: continuous, end behavior, local extrema, and increasing/decreasing intervals.
IW #1:
p. 149/23, 31, 50-53
p. 161/1, 7, 9, 19, 21
Watch this PatrickJMT video (length 7:53) and then write the Intermediate Value Theorem and one example on your IW page
Unit 1: Functions
Wednesday, November 2nd, 2011
After the Supercorrections follow-up test, we finished up the project.
IW:
Finish the project- please email Mr. O'Brien if you are done before Friday midnight.
Halloween, 2011
Today was a day to finish up the projects and any corrections of Supercorrections.
IW:
Correct any corrections of Supercorrections and study for the follow up test on Wednesday. Here is a blank copy of the Unit 1 test.
Finish your project. The final draft is due by midnight Wednesday. Don't forget to read through the rubric one last time.
Thursday, October 27th, 2011
Again, we worked on Supercorrections and project. Those who finished with Supercorrections, submitted them along with the test (unstapled). Again, we used this Google Document to discuss the test. It was also time for the project. Here is a blank copy of the Unit 1 test.
IW:
Work on Supercorrections. They are due by 3 pm Friday.
Work on your project. The rough draft is due by midnight Friday.
Tuesday, October 25th, 2011
Unfortunately, Mr. O'Brien is away today, but you are in the capable hands of the sub. He will give you your test to Supercorrect (the complete explanation of Supercorrections as well as examples that we looked at together in class is available here). Please use this Google Document to discuss the test and ask me questions.
IW:
Work on Supercorrections. They are due by 3 pm Friday.
Work on your project. The rough draft is due by midnight Friday.
You will have time next class to work on your Supercorrections and project.
Friday, October 21st, 2011
Today was test day.
IW:
Work on your project for an hour.
Wednesday, October 19th, 2011
Today was a project day.
IW #17:
Work on your project for one hour.
Monday, October 17th, 2011
We began class by discussing inverses from IW #15. We then took a look at Supercorrections and spent the remainder of the class working on revision problems.
IW #16:
The test covers all of our work in Unit 1 which encompassed the first two chapters in the text. To revise, please do a minimum of 5 problems from p. 69/18-147 and 5 problems from p. 137/1-107. Some of the test questions will come *directly* from these revision problems (the more interesting ones of course, so the more you engage with these problems, the better!
The remaining IW's of Unit 1 are due on test day: #11-#13, #15-#16.
Thursday, October 13th, 2011
We began class by correcting the quiz. We then went over IW #12 and #13. We finished by discussing inverse relations and functions.
We began with the quiz. Following the quiz, we took another look at parametrically defined relations and symmetry and even/odd function tests.
IW #13:
This sheet (no need to print unless you don't have internet access)
Monday, October 3rd, 2011
We began class with a little time to work on the project. We then warmed up with an inequality to solve graphically. After going over IW questions, we explored parametrically defined relations.
IW #12:
Spend at least 20 minutes working on your project
p. 117/49-51
p. 127/15, 17
Thursday, September 29th, 2011
After collecting IW, we warmed up with The Need For Speed (a practice on catching careless errors without a calculator). We then went over our first non-technology quiz. We spent a little time on the quarter projects learning how to enter equations and use Google+. We finished by taking notes on how to solve inequalities graphically and by using critical points and sign analysis.
IW #11:
p. 97/41, 45, 47, 63
p. 109/31, 45
p. 116/25, 27, 29, 35, 39, 41
Tuesday, September 27th, 2011
We began class with the quiz. After that, we took a look at the even answers to IW #9 and discussed some of the word problems.
IW #10:
Make sure you have corrected IW #5-#9 to submit next class
If you don't have your laptop, stop by in study hall, and I'll loan you one of the MDS laptops to use to do and project work.
Get ready for the quarter project (Q1 Project) by doing the following:
Choose a partner (you may opt to work alone if you prefer)
Decide which project you and your partner would like to work on and submit your top 3 choices here. First come first served!
Create a document in Google Docs titled Your Names Q1 Project and share it with obrienbluester@gmail.com.
Friday, September 23rd, 2011
We began class by taking a look at IW #8 together and sketched some parent function graphs to memorize on the board. After some graphisthenics (go ahead, Google it!) and another look at the transformations sheet, we practiced function transformation graphing with a game (submit team answers to each graph here).
IW #9:
p.89/21-39 all
QUIZ on IW #1-#8 next class
Wednesday, September 21st, 2011
We began by solving a challenging equation and learning how technology like wolframalpha.com or the Solver on the calculator can make solving any equation a snap. At this point, everyone should have completed this brief student information sheet. We corrected the quiz, noting the need for efficient solutions, including those that made use of the calculator and/or Geogebra as well as those that do not. We discussed IW #7 and the solutions to the Transformations Sheet and mentioned the idea of a parent function.
We started class by using Geogebra to explore the parabola sheet problems. We then transitioned to exploring transformations of functions using this Geogebra sketch: U1 transformation applet.ggb. A summary of the transformation notes is available here.
IW #6:
Transformation sheet
QUIZ on IW #1-#5 on Monday
Tuesday, September 13th, 2011
We began by checking the common algebra errors sheet in pairs. We then took a brief look at the proof and result from p. 45/84. We corrected the quiz and ended class with an investigation into what makes a parabola a parabola. Here are the notes from the board.
IW #5:
Parabola sheet
Friday, September 9th, 2011
We began class by finishing the final IW #2 questions, thereby revising the good calculator usage. We then took the quiz and ended by discussing IW #3 using Geogebra.
IW #4:
p. 45/84
Common Algebra Errors sheet
Wednesday, September 7th, 2011
We began class by finding the domain and range of an interesting function algebraically and graphically. We discussed how to use the equation-graph-table triumverate on the graphing calculator and then looked at some questions from IW #2. We learned how to use the table to get an appropriate viewing window and how to use Calc-Intersect. We then took some notes on linear functions using a problem on Geogebra, including slope intercept form, standard form, point-slope form, horizontal and vertical lines, parallel/perpendicular slope relationship, and linear inequalities.
IW #3:
QUIZ next class on IW #1 and IW #2.
Look over IW #1 and IW #2 and make sure they are checked and corrected. If there are any errors remaining, stop by MDS to fix them up! You will be able to use them on the quiz next class.
p. 42/5, 11, 19, 27, 31, 43, 45, 65, 83
Thursday, September 1st, 2011
We began class with a function matching game to talk about the graph-equation-table connection. This led to a discussion of domain and range. We explored three interesting functions using this applet and our graphing calculators. We discussed the responsibility and independent work rubrics and went over IW #1, answering all questions in preparation for the quiz next Friday.
IW #2:
p. 30/21, 39, 45, 50, 51, 52, 53, 54, 58, 59, 60
Tuesday, August 30th, 2011
We began class with some introductions and a discussion of the course methodology, including what Pre-AP Calculus is all about, expectations for class, the importance of independent work, how to get help, and more. We then discussed functions by examining this applet. The importance of viewing functions numerically and graphically is the reason each of us must have a graphics calculator for this class- and the future.
IW #1:
Take a look through sections 1.1 and 1.2 in your textbook to remind yourself of some of what you're expected to remember from previous math courses. If there's any topic or formula that you'd like to review in class, just send me an email or let me know at the start of next class.
p. 30/3, 5, 7, 9, 11
Give the parent/guardian letter to your parent/guardian (a copy is available on the home page).
Table of Contents
Unit 4: Advanced Trigonometry
End of Year
Here is the Final Exam study guide.IW:
Friday, May 25th, 2012
We worked on the project.IW:
Wednesday, May 23rd, 2012
Today was the Finely Crafted Opportunity Day.IW:
Monday, May 21st, 2012
Today was a revision day for the test.IW #14:
Wednesday, May 16th, 2012
Today was project day.IW:
Monday, May 14th, 2012
We took the IW #13 quiz and those that wanted then took the re-quiz. Others worked on the project.IW:
Thursday, May 10th, 2012
We warmed up with some IW #13 questions- without technology. We then discussed the IW and corrected the quiz. We spent the remainder of class working on the project.IW:
Tuesday, May 8th, 2012
After the IW quiz, we worked on IW #13 in groups. The assessment on IW #13 will be a quiz *without* technology where you will need to sketch graphs, write equations, find intercepts, etc. of polar graphs from IW #13. You will be able to use IW #13 on the quiz, so be sure you have thoroughly investigated the polar graphs and taken good notes. Feel free to also bring any questions to next class.IW:
Friday, May 4th, 2012
We worked on IW #13, a polar graphing investigation.IW #13:
Wednesday, May 2nd, 2012
We began class with a vector warm-up and then took a further look at addition and subtraction geometrically with this applet. We discussed the IW and then examined polar coordinates and polar graphing.IW #12:
Monday, April 30th, 2012
We by correcting the IW quiz and discussing the cool complex number assignment. This led us to a discussion of vectors.IW #11:
Thursday, April 26th, 2012
We began class with the IW quiz. We then went over the IW questions, focusing on geometric interpretations of De-Moivre's Theorem.IW #10:
Tuesday, April 24th, 2012
We began class by going over the IW quiz. We then discussed the IW, focusing on how to use the calculator as well as how diagrams and reasoning are better than formulas. We then worked on the IW #9 packet.IW #9:
Friday, April 13th, 2012
We began class with the IW quiz. We then went over the IW questions and learned how trigonometry is used with complex numbers.IW #8:
Wednesday, April 11th, 2012
We began by finding an enveloping function for the sum of two sine functions which lead us to the Sum to Product identities. After we went through the proofs from IW #6, we proved a Product to Sum identity and used it to prove the identity needed in the warm-up. We also learned how to find the exact values of the first question from the Unit 4 Quiz #1 without using technology. We finished by looking at how to solve trig equations algebraically.IW #7:
Monday, April 9th, 2012
We began class by proving four trig identities, proving we could do so without crying. We then went over the IW questions and the IW quiz. We spent the remainder of class working on IW #6, deriving sum/difference, double, and half angle identities.IW #6:
Thursday, April 5th, 2012
We had our IW quiz and then worked some more on proving identities.IW #5:
Tuesday, April 3rd, 2012
We began class by learning about how to verify trig identities. Here are a set of guidelines to avoid tears... We spent the remainder of the class discussing the previous independent work questions.IW #4:
Friday, March 30th, 2012
We began with the first several questions of IW #3 and then discussed IW #2. For the remainder of class, we worked on the IW #3 sheet.IW #3:
Wednesday, March 28th, 2012
We began class by checking answers to IW #1 and discussing wave packets. We then transitioned to inverse trig relations. We used Geogebra to discover how to restrict domains to create functions. We then tried p. 395/42 and 49 from the IW, noting that inverse trig functions were just angles.IW #2:
Monday, March 26th, 2012
We began by finding a plausible expression to generate this graph:We then went over the Supercorrection follow up test. We spent the remainder of the period investigating trig wave functions with the IW packet.
IW #1:
Unit 3: Trigonometric Functions
Thursday, March 22nd, 2012
We took the follow up test and finished the project.IW:
Tuesday, March 20th, 2012
We worked on the project.IW:
Thursday, March 15th, 2012
We worked on the projects.IW:
Tuesday, March 13th, 2012
We worked on Supercorrections.IW:
Friday, March 9th, 2012
We worked on Supercorrections.IW:
Wednesday, March 7th, 2012
We finished the test and began Supercorrections.IW:
Monday, March 5th, 2012
Today was test day!IW:
Thursday, March 1st, 2012
Snow day! Test postponed until Monday.Optional IW:
Tuesday, February 28th, 2012
Today was our revision day. We warmed up by finding a couple plausible periodic functions from graphs. We then corrected the quiz and went over IW questions and general revision. We finished by watching the Tau Day video again and discussing the trig segments.IW #11:
Friday, February 17th, 2012
We began class with the quiz: Quizlet question #1. We then proved the Law of Cosines and went over the IW. We also took a look at the Tau Manifesto.IW #10:
Wednesday, February 15th, 2012
We began class with this exploration in Geogebra. After proving the Law of Sines, we derived a formula for the area of a triangle given two sides and an included angle, and we discussed the IW and The Ambiguous Case (Eben's applet & Kyle's Applet). We then corrected the quiz and took a look at six trig segments in the unit circle- neato! We finished class by deriving the Law of Cosines.IW #9:
Monday, February 13th, 2012
We began class with the IW quiz. Following the quiz, we corrected the IW and learned a way to solve a non-right angled triangle using the Law of Sines.IW #8:
Thursday, February 9th, 2012
In preparation for the next quiz on which a portion will be no calculator/no unit circle, we once again began class with the little practice quiz on the six trig functions of the common angles and did a little stand-up practice. We then discussed the quiz from last class and went over IW questions. The remainder of the class was spent working trig application problems.IW #7:
Tuesday, February 7th, 2012
We again began class with the little practice quiz on the six trig functions of the common angles. We then took the quiz on IW #1 and #4 and went over questions from IW #5. We then took a little break from all this heavy full circle trig by revisiting some nice, friendly right triangle trig.IW #6:
Friday, February 3rd, 2012
We began class with a game of Around The World to practice our common trig values and then continued with five minutes of the little practice quiz on the six trig functions of the common angles. We then corrected the quiz and discussed the IW. We noted how trig equations can be solved with either the unit circle or a graph and how the symmetry of the trig waves along with five key points and a labeled scale makes any trig graphing task a snap. We then explored how the other four trig function graphs can be derived from the sine and cosine waves. Our discussion included a look at domain, range, period, and vertical asymptotes.IW #5:
Wednesday, February 1st, 2012
We began class with a little practice quiz on the six trig functions of the common angles. This led us to a review of the trig properties from last class. We then took the quiz on IW #1 and #2 and went over questions from IW #3. We used this Geogebra sketch to explore the graphs of the sine and cosine function. We discussed period, amplitude, and even/odd, and finished by looking at transformations of the graphs.IW #4:
Monday, January 30th, 2012
We began class with a little practice quiz converting between the common degree and radian values. We then discussed the independent work, learning how easy it is to find arc length (and sector area) when working in radians. We took a closer look at the Unit Circle and how its coordinates are found and then defined the cosine and sine functions using points on this wonderful circle. We defined the other four trig functions which led to three sets of identities: the reciprocal, quotient, and Pythagorean. We finished by discussing the importance of the common trig values.IW #3:
Thursday, January 26th, 2012
We began class by discussing Francois and his pedometer. We then took some trig notes using this introductory packet.IW #2:
Tuesday, January 24th, 2012
We began class with an individual reflection on the first semester, and then in groups of three or four, we came up with some pieces of advice for success in an O'Brien math classroom. We then discussed some of the midterm and introduced our new unit on trigonometry.IW #1:
Unit 2: Polynomial, Rational, Radical, Exponential, Logarithmic Functions
Midterm Answer Sheet
Here it is.Midterm Revision Guide
Here it is.Supercorrection Follow-up
Here is a blank copy of the Finely Crafted Unit 2 Opportunity Day: U2T pap.pdfMonday, January 3, 2012 – Friday, January 13, 2012
We worked on Supercorrections and the quarter project- see deadlines in iCal.Tuesday, December 20th, 2011
Today was the Opportunity Day.IW:
Friday, December 16th, 2011
We worked on our second quarter project..IW:
Wednesday, December 14th, 2011
Today was our revision day.IW:
Monday, December 12th, 2011
After the quiz, we took a look at the acoustic function that the Windplanners used to present their case to the school board. We also discussed the IW.IW #12:
Thursday, December 8th, 2011
We warmed up and discovered some interesting ways to perceive exponential and logarithmic functions. After discussing the IW's, we corrected the quiz.IW #11:
Tuesday, December 6th, 2011
We began class with the quiz and then corrected the IW. This led us to a discussion of the inverse of an exponential function: a new parent function!IW #10:
Friday, December 2nd, 2011
We began by exploring the end behavior of an interesting function: (1 + 1/x)^x. Who wins as x goes to infinity- the 1/x going to zero or the massively powerful power of x?!? We also listened to this radio segment from NPR this week. We then corrected the quiz and discussed the IW. We ended class by discussing compound interest, connecting it all back to our warm-up function.IW #9:
Wednesday, November 30th, 2011
We began class with the quiz. After the quiz, we took a brief look at IW questions. We then thought about this question:- If a piece of paper could be folded in half fifty times, how high would the stack of paper be? For more on this problem, click here. Have you heard that it is impossible to fold a piece of paper more than eight times? If so, click here .
This led us to define our next parent function, the exponential.IW #8:
Monday, November 28th, 2011
We began class by creating a couple of rational functions. We then corrected the quiz and discussed IW #5 & #6.IW #7:
Monday, November 21st, 2011
We began class with the quiz. We discussed the IW and created some cool rational functions.IW #6:
Thursday, November 17th, 2011
We warmed up with a rational function transformation question. After correcting the quiz and discussing the IW, we explored rational functions by using Geogebra, our hand graphing skills, and our rational function building skills.IW #5:
Tuesday, November 15th, 2011
We began class with the quiz. We looked at IW questions and the "build a polynomial" extra credit from last class, and then ended class with some notes on rational functions, including horizontal and vertical asymptotes from a graphic and numeric perspective.IW #4:
Thursday, November 10th, 2011
We began class with a warm up equation, finding *all* the zeros, including complex zeros. This led to some notes on complex conjugates, the Fundamental Theorem of Algebra, and multiplicity of zeros. After correcting the IW, we participated in some polynomial forming extra credit (submit your polynomials here).IW #3:
Tuesday, November 8th, 2011
We began class by using a warm-up question (photo of the board here) and IW #1 to discuss good graphing calculator viewing window tricks: using the table, using Zbox, Zfit, etc. We corrected the Supercorrection Follow-up test, took a look at Mr. O'Brien's online grade calculator, and discussed IOU's. We then discussed zeros which led to a look at the Rational Zero Test, polynomial long division and synthetic division, the Remainder Theorem, the Factor Theorem, and the complex numbers (photos of the board here, here, here, here, and here).IW #2:
Friday, November 4th, 2011
Today was the start of our next unit. We began by creating a general 5th degree polynomial function in Geogebra and explored it. We learned some new vocabulary: continuous, end behavior, local extrema, and increasing/decreasing intervals.IW #1:
Unit 1: Functions
Wednesday, November 2nd, 2011
After the Supercorrections follow-up test, we finished up the project.IW:
Halloween, 2011
Today was a day to finish up the projects and any corrections of Supercorrections.IW:
Thursday, October 27th, 2011
Again, we worked on Supercorrections and project. Those who finished with Supercorrections, submitted them along with the test (unstapled). Again, we used this Google Document to discuss the test. It was also time for the project. Here is a blank copy of the Unit 1 test.IW:
Tuesday, October 25th, 2011
Unfortunately, Mr. O'Brien is away today, but you are in the capable hands of the sub. He will give you your test to Supercorrect (the complete explanation of Supercorrections as well as examples that we looked at together in class is available here). Please use this Google Document to discuss the test and ask me questions.IW:
Friday, October 21st, 2011
Today was test day.IW:
Wednesday, October 19th, 2011
Today was a project day.IW #17:
Monday, October 17th, 2011
We began class by discussing inverses from IW #15. We then took a look at Supercorrections and spent the remainder of the class working on revision problems.IW #16:
Thursday, October 13th, 2011
We began class by correcting the quiz. We then went over IW #12 and #13. We finished by discussing inverse relations and functions.IW #15:
Tuesday, October 11th, 2011
Today was a project day.IW #14:
Wednesday, October 5th, 2011
We began with the quiz. Following the quiz, we took another look at parametrically defined relations and symmetry and even/odd function tests.IW #13:
Monday, October 3rd, 2011
We began class with a little time to work on the project. We then warmed up with an inequality to solve graphically. After going over IW questions, we explored parametrically defined relations.IW #12:
Thursday, September 29th, 2011
After collecting IW, we warmed up with The Need For Speed (a practice on catching careless errors without a calculator). We then went over our first non-technology quiz. We spent a little time on the quarter projects learning how to enter equations and use Google+. We finished by taking notes on how to solve inequalities graphically and by using critical points and sign analysis.IW #11:
Tuesday, September 27th, 2011
We began class with the quiz. After that, we took a look at the even answers to IW #9 and discussed some of the word problems.IW #10:
Friday, September 23rd, 2011
We began class by taking a look at IW #8 together and sketched some parent function graphs to memorize on the board. After some graphisthenics (go ahead, Google it!) and another look at the transformations sheet, we practiced function transformation graphing with a game (submit team answers to each graph here).IW #9:
Wednesday, September 21st, 2011
We began by solving a challenging equation and learning how technology like wolframalpha.com or the Solver on the calculator can make solving any equation a snap. At this point, everyone should have completed this brief student information sheet. We corrected the quiz, noting the need for efficient solutions, including those that made use of the calculator and/or Geogebra as well as those that do not. We discussed IW #7 and the solutions to the Transformations Sheet and mentioned the idea of a parent function.IW #8:
Monday, September 19th, 2011
We began by answering this question and completing this brief student information sheet. We then took the quiz. We took brief notes on function composition and then checked the transformations sheet using these 8 Geogebra sketches. We discussed how in general 2f(x) ≠ f(2x) and how points can be used to identify transformations.IW #7:
Thursday, September 15th, 2011
We started class by using Geogebra to explore the parabola sheet problems. We then transitioned to exploring transformations of functions using this Geogebra sketch: U1 transformation applet.ggb. A summary of the transformation notes is available here.IW #6:
Tuesday, September 13th, 2011
We began by checking the common algebra errors sheet in pairs. We then took a brief look at the proof and result from p. 45/84. We corrected the quiz and ended class with an investigation into what makes a parabola a parabola. Here are the notes from the board.IW #5:
Friday, September 9th, 2011
We began class by finishing the final IW #2 questions, thereby revising the good calculator usage. We then took the quiz and ended by discussing IW #3 using Geogebra.IW #4:
Wednesday, September 7th, 2011
We began class by finding the domain and range of an interesting function algebraically and graphically. We discussed how to use the equation-graph-table triumverate on the graphing calculator and then looked at some questions from IW #2. We learned how to use the table to get an appropriate viewing window and how to use Calc-Intersect. We then took some notes on linear functions using a problem on Geogebra, including slope intercept form, standard form, point-slope form, horizontal and vertical lines, parallel/perpendicular slope relationship, and linear inequalities.IW #3:
Thursday, September 1st, 2011
We began class with a function matching game to talk about the graph-equation-table connection. This led to a discussion of domain and range. We explored three interesting functions using this applet and our graphing calculators. We discussed the responsibility and independent work rubrics and went over IW #1, answering all questions in preparation for the quiz next Friday.IW #2:
Tuesday, August 30th, 2011
We began class with some introductions and a discussion of the course methodology, including what Pre-AP Calculus is all about, expectations for class, the importance of independent work, how to get help, and more. We then discussed functions by examining this applet. The importance of viewing functions numerically and graphically is the reason each of us must have a graphics calculator for this class- and the future.IW #1: